Question

Find the remainder when f(x) = f( x)= 4x^3- 12x^2 + 14x-3 is divided by g(x)=(2x-1)

Answer 1

let g (x) =0
2x-1=0
2x=1
x=1/2
f (1/2)=4(1/2)^3 - 12 (1/2)^2+14 (1/2)-3
= 4 (1/8)-12 (1/4)+14 (1/2)-3
=1/2-3+7-3
= 1-12+14-6/2
=-11+8
=-3/2

OR
1/2-3+7-3
-2+4
2/2 =0

I'm not sure but one them will be correct maybe just check the answer and you can write that one if it is right

Answer 2

using remainder theoram,
2x-1=0
2x=1
x=1/2
f(1/2)= 4(1/2)^3-12(1/2)^2+14(1/2)-3
= 4(1/8)-12(1/4)+14(1/2)-3
= 1/2-3+7-3
= 1/2 +1
taking LCM= 2,
= 1/2+2/2
= 3/2.
hence, remainder = 3/2.